U. K. Misra

Deferred weighted -statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

Abstract Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and 𝒜 {\mathcal{A}} -statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted 𝒜 {\mathcal{A}} -statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t 2 {t^{2}} defined on a Banach space C ⁢ [ 0 , 1 ] {C[0,1]} for a sequence of (presumably new) positive linear operators based upon ( p , q ) {(p,q)} -Lagrange polynomials. Furthermore, we investigate the deferred weighted 𝒜 {\mathcal{A}} -statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

Fuzzy Economic Production Quantity Model with Time Dependent Demand Rate

Background: In this paper, an economic production quantity mod el is considered under a fuzzy environment. Both the demand cost and holding cost a re considered using fuzzy pentagonal numbers. The S igned Distance Method is used to defuzzify the total cost function. Methods: The results obtained by these methods are compared with the help of a numerical example. Sensitivity analysis is also carried out to explore the effect of changes in the values of some of the system para meters. Results and conclusions: The fuzzy EPQ model with time dependent demand rat e was presented together with the possible implementation. The behavior of changes in parameters was analyzed. The possible extension of the implementation of this method was presented.

Local property of factored Fourier series by indexed Norlund summability

L. D. Jena Department of Mathematics, Ravenshaw University, Cuttack, Odisha, India S. K. Paikray Department of Mathematics, VSSUT, Burla, Odisha, India Corresponding author M. Dash Department of Mathematics, Ravenshaw University, Cuttack, Odisha, India U. K. Misra Department of Mathematics, NIST, Berhampur, Odisha, India Copyright

A Tauberian Theorem for Double Cesàro Summability Method

We have generalized Littlewood Tauberian theorems for summability of double sequences by using oscillating behavior and de la Vallee-Poussin mean. Further, the generalization of summability from summability is given as corollaries which were earlier established by the authors.

Approximation of signals belonging to generalized Lipschitz class using -summability mean of Fourier series

Degree of approximation of functions of different classes has been studied by several researchers by different summability methods. In the proposed paper, we have established a new theorem for the approximation of a signal (function) belonging to the -class by -product summability means of a Fourier series. The result obtained here, generalizes several known theorems.

Trigonometric approximation of the conjugate series of a function of generalized Lipchitz class by product summability

Trigonometric Fourier approximation and Lipchitz class of function had been introduced by Zygmund and McFadden respectively. Dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. have established certain theorems. Extending their results, in this paper a theorem on trigonometric approximation of conjugate series of Fourier series of a function \( f \in \,Lip\,\left( {\alpha ,r} \right) \) by product summability (E, s) (N, p n , q n ) has been established.

Degree of Approximation of Conjugate Series of a Fourier Series by Hausdroff and Norlund Product Summability

Lipchitz class of function had been introduced by McFadden. Recently dealing with degree of approximation of conjugate series of a Fourier series of a function of Lipchitz class Misra et al. and Paikray et al. have established certain theorems. Extending their results, in this paper a theorem on degree of approximation of a function f belongs to a class of \( Lip\left( {\alpha ,r} \right)\) by using product summability \( \left( {E,q} \right)\left( {N,p_{n} } \right) \) has been established.